Chapter 1.4 ElementaryMatrices

We say a and b are row equivalent if each can be

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: nt if each can be obtained from the other by a finite sequence of row operations. Rephrase (c) of the theorem: Theorem An n × n matrix A is invertible if and only if A is row equivalent to In . Outline Elementary Matrix Inverse of an Elementary Matrix The Inverse of a Matrix Finding the Inverse of a Matrix Theorem If A is an invertible n × n matrix, and C = [A | In ], then rref (C ) = [In | A−1 ]. Proof. Er Er −1 · · · E1 A = In , where Ei is the elementary matrix corresponding to the i th elementary row operation in the sequence required to obtain In . Therefore, A−1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online